Download Distance determination for RAVE stars using stellar models

Astronomy
&
Astrophysics
A&A 511, A90 (2010)
DOI: 10.1051/0004-6361/200912471
c ESO 2010
Distance determination for RAVE stars using stellar models
M. A. Breddels1 , M. C. Smith2,3,1 , A. Helmi1 , O. Bienaymé4 , J. Binney5 , J. Bland-Hawthorn6 , C. Boeche7
B. C. M. Burnett5 , R. Campbell7 , K. C. Freeman8 , B. Gibson9 , G. Gilmore3 , E. K. Grebel10 , U. Munari11 ,
J. F. Navarro12 , Q. A. Parker13 G. M. Seabroke14 A. Siebert4 , A. Siviero11,7 , M. Steinmetz7 , F. G. Watson6 ,
M. Williams7 R. F. G. Wyse15 , and T. Zwitter16
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Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
e-mail: [email protected]
Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, PR China
Institute of Astronomy, University of Cambridge, Cambridge, UK
Université de Strasbourg, Observatoire Astronomique, Strasbourg, France
Rudolf Peierls Centre for Theoretical Physics, Oxford, UK
Anglo-Australian Observatory, Sydney, Australia
Astrophysikalisches Institut Potsdam, Potsdam, Germany
RSAA, Australian National University, Canberra, Australia
University of Central Lancashire, Preston, UK
Astronomisches Rechen-Institut, Center for Astronomy of the University of Heidelberg, Heidelberg, Germany
INAF, Astronomical Observatory of Padova, Asiago station, Italy
University of Victoria, Victoria, Canada
Macquarie University, Sydney, Australia
e2v Centre for Electronic Imaging, Planetary and Space Sciences Research Institute, The Open University, Milton Keynes, UK
Johns Hopkins University, Baltimore, MD, USA
Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
Received 12 May 2009 / Accepted 15 December 2009
ABSTRACT
Aims. We develop a method for deriving distances from spectroscopic data and obtaining full 6D phase-space coordinates for the
RAVE survey’s second data release.
Methods. We used stellar models combined with atmospheric properties from RAVE (effective temperature, surface gravity and
metallicity) and (J − Ks ) photometry from archival sources to derive absolute magnitudes. In combination with apparent magnitudes,
sky coordinates, proper motions from a variety of sources and radial velocities from RAVE, we are able to derive the full 6D phasespace coordinates for a large sample of RAVE stars. This method is tested with artificial data, Hipparcos trigonometric parallaxes and
observations of the open cluster M 67.
Results. When we applied our method to a set of 16 146 stars, we found that 25% (4037) of the stars have relative (statistical) distance
errors of <35%, while 50% (8073) and 75% (12 110) have relative (statistical) errors smaller than 45% and 50%, respectively. Our
various tests show that we can reliably estimate distances for main-sequence stars, but there is an indication of potential systematic
problems with giant stars owing to uncertainties in the underlying stellar models. For the main-sequence star sample (defined as those
with log(g) > 4), 25% (1744) have relative distance errors <31%, while 50% (3488) and 75% (5231) have relative errors smaller than
36% and 42%, respectively. Our full dataset shows the expected decrease in the metallicity of stars as a function of distance from
the Galactic plane. The known kinematic substructures in the U and V velocity components of nearby dwarf stars are apparent in
our dataset, confirming the accuracy of our data and the reliability of our technique. We provide independent measurements of the
orientation of the UV velocity ellipsoid and of the solar motion, and they are in very good agreement with previous work.
Conclusions. The distance catalogue for the RAVE second data release is available at http://www.astro.rug.nl/~rave, and will
be updated in the future to include new data releases.
Key words. methods: numerical – methods: statistical – stars: distances – Galaxy: kinematics and dynamics – Galaxy: structure
1. Introduction
The spatial and kinematic distributions of stars in our Galaxy
contain a wealth of information about its current properties, its
history and evolution. This phase-space distribution is a crucial
ingredient if we are to build and test dynamical models of the
Milky Way (e.g. Binney 2005, and references therein). More
directly, the kinematics of halo stars can be used to trace the
Galaxy’s accretion history (Helmi & White 1999), as has been
shown to good effect in many subsequent studies (e.g. Helmi
et al. 1999; Kepley et al. 2007; Smith et al. 2009). There is also
much to learn from the phase-space structure of the disk, where it
is possible to identify substructures due to both accretion events
and dynamical resonances (e.g. Dehnen 2000; Famaey et al.
2005; Helmi et al. 2006) or learn about the mixing processes
that influence the chemical evolution of the disk (e.g. Roškar
et al. 2008; Schönrich & Binney 2009).
Article published by EDP Sciences
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A&A 511, A90 (2010)
To fully exploit this rich resource, we need to analyse the full
six-dimensional phase-space distribution, which clearly cannot
be done without a reliable estimate of the distances to the stars
under consideration. Therefore obtaining accurate distances and
velocities for a representative sample of stars in our Galaxy will
be essential if we are to understand both the structure of our own
Galaxy and galaxy formation in general.
The most dramatic recent development in this field was the
Hipparcos satellite mission (ESA 1997; Høg et al. 2000), which
carried out an astrometric survey of stars down to V ∼ 12 mag
with accuracies of up to 1 mas. This catalogue enabled the
distances of ∼10 000 stars to be measured using the trigonometric parallax technique, with parallax errors of less than 5%
(van Leeuwen 2007a,b). However, in general the resulting parallaxes only probe out to a couple of hundred parsec and are
limited to the brightest stars.
This limitation of the trigonometric parallax method led researchers to attempt other techniques for calculating distances.
One promising avenue is the study of pulsating variable stars,
such as RR Lyraes or Cepheids, for which it is possible to accurately determine distances using period-luminosity relations
(see, for example, the reviews of Gautschy & Saio 1995, 1996).
These have been used effectively to probe the structure of our
Galaxy, in particular the study of the old and relatively metalpoor RR Lyrae stars (Vivas et al. 2001; Kunder & Chaboyer
2008; Watkins et al. 2009).
Although pulsating variables can provide accurate tracer
populations, the numbers of such stars is clearly limited; ideally
we would like to determine distances for large numbers of stars
and not just specific populations. As a consequence there have
been numerous studies utilising photometric distance determinations, where one estimates the absolute magnitude of a star from
its colour. The efficacy of this method can be seen from the work
of Siegel et al. (2002) and Jurić et al. (2008), who both used this
technique to model the stellar density distribution of the Galaxy.
Another striking example of the power of this technique was presented by Belokurov et al. (2006), where halo turn-off stars were
used to illuminate a host of substructures in the Galactic halo.
The strength of photometric distances is that they can be
constructed for a wide range of stellar populations. An important recent study was carried out by Ivezić et al. (2008). In
this work they took high-precision multi-band optical photometry from the Sloan Digital Sky Survey (SDSS; Abazajian et al.
2009) and constructed a photometric distance relation for F- and
G-type dwarfs, using colours to identify main-sequence stars
and estimate metallicity. Globular clusters were used to calibrate
their photometric relation, resulting in distance estimates accurate to ∼15 per cent. This is only possible due to the extremely
well-calibrated SDSS photometry and, in any case, is only applicable to F- and G-type dwarfs. To determine distances for entire surveys (with a wide range of different stellar classes and
populations) requires complex multi-dimensional algorithms. In
this paper we develop such a technique to estimate distances for
stars using photometry in combination with stellar atmosphere
parameters derived from spectra.
One of the motivations behind our study is so that we can
complement the Radial Velocity Experiment (RAVE Steinmetz
et al. 2006; Zwitter et al. 2008). This project, which started in
2003, is currently measuring radial velocities and stellar atmosphere parameters (temperature, metallicity and surface gravity)
for stars in the magnitude range 9 < I < 12. By the time it
reaches completion in ∼2011 it is hoped that RAVE will have
observed up to one million stars, providing a dataset that will be
of great importance for Galaxy structure studies. A number of
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publications have already made use of this dataset (e.g. Smith
et al. 2007; Klement et al. 2008; Munari et al. 2008; Siebert
et al. 2008; Veltz et al. 2008), but to fully utilise the kinematic
information we crucially need to know the distances to the stars.
Unfortunately, most of the stars in the RAVE catalogue are too
faint to have accurate trigonometric parallaxes, hence the importance of a reliable and well-tested photometric/spectroscopic
parallax algorithm. When distances are combined with archival
proper motions and high precision radial velocities from RAVE,
this dataset will provide the full 6D phase-space coordinates for
each star. Clearly such an algorithm for estimating distances will
be a vital tool when carrying out kinematic analyses of large
samples of Galactic stars, not just for the RAVE survey but for
any similar study.
The future prospects for distance determinations are very
promising. In the next decade the Gaia satellite (Perryman et al.
2001) will observe up to 109 stars with exquisite astrometric precision. The mission is due to start in 2012, but a final data release
will not arrive until near the end of the decade at the earliest.
Furthermore, as with any such magnitude limited survey, there
will be a significant proportion of stars for which their distances
are too great for accurate trigonometric parallaxes to be determined. Therefore, although Gaia will revolutionise this field, it
will not close the chapter on distance determinations for stars
in the Milky Way and so photometric parallax techniques will
remain of crucial importance.
In this paper we present our algorithm for determining distances, which we construct using stellar models. When we apply
this method to the RAVE dataset we are able to reproduce several known characteristics of the kinematics of stars in the solar
neighbourhood. In Sect. 2, we present a general introduction.
We discuss the connection between stellar evolution theory, stellar tracks and isochrones to gain insight in these topics before
presenting our statistical methods for the distance determination
and testing the method using synthetic data. In Sect. 3 we apply
the method to the RAVE dataset and compare the distances to
external determinations, namely stars in the open cluster M 67
and nearby stars with trigonometric parallaxes from Hipparcos.
Results obtained from the phase-space distribution are presented
in Sect. 4 to check whether the data reflect known properties
of our Galaxy. We present a discussion of the uncertainties and
limitations of the method in Sect. 5 and conclude with Sect. 6.
2. Method for distance determination
2.1. Stellar models and observables
Stellar models are commonly used to estimate distances, for instance in main-sequence fitting. Such methods work for collections of stars, but models can also be used to infer properties of
individual stars, such as ages (Pont & Eyer 2004; Jorgensen &
Lindegren 2005; da Silva et al. 2006). In our analysis we utilise
this approach, combining stellar parameters (temperature, metallicity and surface gravity) with photometry to estimate a star’s
absolute magnitude.
The evolution of a star is fully determined by its mass
and initial chemical composition (e.g. Salaris & Cassisi 2005).
Stellar tracks and isochrones can be seen (in a mathematical
sense) as a function (F ) of alpha-enhancement ([α/Fe]), metallicity (Z), mass (m) and age (τ) that maps onto the observables:
absolute magnitude (Mλ ), surface gravity (log(g)), effective temperature (T eff ), and colours, i.e.
F ([α/Fe], Z, τ, m) → (Mλ , log(g), T eff , colours, . . .).
(1)
M. A. Breddels et al.: Distance determination for RAVE stars
Fig. 1. log(g) versus log(T eff ) plot for isochrones from 0.01−15 Gyr
spaced logarithmically, for [M/H] = 0 and [α/Fe] = 0. Colour indicates
the absolute magnitude in the J band.
In particular, an isochrone is the function I(m) of mass, which
is obtained from F by keeping all other variables constant.
Assuming solar α-abundance, [α/Fe]= 0, we define the function F0 (Z, τ, m), which is F with [α/Fe] fixed at 0,
F0 (Z, τ, m) = F (Z, τ, m)|[α/Fe]=0
→ (Mλ , log(g), T eff , colours...).
(2)
Therefore the isochrones or stellar tracks from a given model
can be seen as samples from the theoretical stars defined
by F0 (Z, τ, m). Throughout this paper we assume solar-scaled
metallicities, which means that [α/Fe] = 0 and [M/H] =
[Fe/H], where [M/H] is defined as log(Z/Z ).
For our study we use the Y 2 (Yonsei-Yale) models
(Demarque et al. 2004). These models can be downloaded from
the Y 2 website1 , where also an interpolation routine is available,
called YYmix2. It should be noted that these models ignore any
element diffusion that may take place in the stellar atmosphere
(see, for example, Tomasella et al. 2008).
A sample of theoretical “model stars” from these Y 2 models
are shown in Fig. 1. Each model star is represented as a dot and
the connecting lines correspond to the isochrones of different
ages. In Fig. 2 we show the same isochrones as Fig. 1, illustrating the relation between M J and T eff , and between M J and
log(g) separately. Clearly, for a given T eff , log(g) and [M/H] it
is not possible to infer a unique M J (i.e. the function F0 is not
injective). This can be seen most clearly in Fig. 1, where around
log(T eff ) = 3.8, log(g) = 4 the isochrones overlap. However, this
is also evident in other regions; for example in the top panels
of Fig. 2 the isochrones are systematically shifted as metallicity
goes from 0 to −2. Because we are unable to determine a unique
M J for a given star we are forced to adopt a statistical approach,
i.e. obtaining a probability distribution for M J .
From Fig. 2 we can see how errors in the observables log(g)
and T eff affect the uncertainty in the absolute magnitude (M J in
this example). The middle row in Fig. 2 shows that the value
1
http://www-astro.physics.ox.ac.uk/~yi/yyiso.html
Fig. 2. Isochrones for [α/Fe] = 0, [M/H] = 0 (left column) and
[M/H] = −2 (right column), ages ranging from 0.01−15 Gyr spaced
logarithmically. The dashed line indicates the youngest (0.01 Gyr)
isochrone. Top row: similar to Fig. 1, shown for completeness. Middle
row: MJ is best restricted by log(g) for RGB stars. Bottom row: MJ is
best restricted by T eff for main-sequence stars.
of M J is better defined by log(g) for red giant branch (RGB)
stars than for main-sequence stars, independently of their metallicity. On the other hand, the bottom row of Fig. 2 shows that T eff
essentially determines M J for main-sequence stars, again independently of metallicity. We therefore expect that a small error
in log(g) will give better absolute magnitude estimates for RGB
stars, while a small error in T eff will have a similar effect on
main-sequence stars. We also expect this not to be strongly dependent on metallicity.
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A&A 511, A90 (2010)
2.2. Description of the method
We now outline the method that we use to estimate the probability distribution function (PDF) for the absolute magnitude
(or, equivalently, the distance). Previous studies have employed
similar techniques to determine properties of stars using stellar
models. A selection of such work can be found in the following
references: Pont & Eyer (2004); Jorgensen & Lindegren (2005);
da Silva et al. (2006).
Our method requires a set of model stars. As was discussed in Sect. 2.1, we have chosen to use the Y 2 models
(Demarque et al. 2004). We generate our set of isochrones using the YYmix2 interpolation code. The set consists of 600
isochrones, with 40 different ages, spaced logarithmically between 0.01 and 15.0 Gyr, and 15 different metallicities with
0.25 dex separation (corresponding to 1 sigma in [M/H] for the
RAVE data; see Sect. 3.1) between [M/H] = −2.5 and [M/H]
= 1.0. The separation between the points of the isochrones has
been visually inspected and is, in general, smaller than the errors in T eff and log(g). These isochrones do not track the evolution beyond the RGB tip. We only use the isochrones with
[α/Fe] = 0 because our observational data do not allow an accurate measurement of [α/Fe] and for most of our stars we expect [α/Fe] ≈ 0. Later, in Sect. 2.3, we show that assuming
[α/Fe] = 0 for stars having [α/Fe] > 0 does not introduce any
noticeable bias in our results.
Let us suppose we have measured the following parameters
for a sample of stars: T eff , log(g), [M/H] and (J − Ks ). Each of
these quantities will have associated uncertainties due to measurement errors (σT eff , σlog(g) , σ[M/H] and σ(J−Ks ) ), which we assume are Gaussian. For each observed star we first need to obtain
the closest matching model star, which we do by minimising the
usual χ2 statistic,
χ2model =
n
(Ai − Ai,model )2
i=1
σ2Ai
,
(3)
where Ai corresponds to our observable parameters (i.e. n = 4 in
this case) and Ai,model the corresponding parameters of the model
star, as given by the set of isochrones. By minimising Eq. (3),
we obtain the parameters for the most-likely model star, denoted
A1 , ..., An .
Having identified the most probable model, we generate
5000 realisations of the observations that could be made of this
model star by sampling Gaussian distributions in each observable that are centred on the model values, with the dispersion in
each observable equal to the errors in that quantity2. By drawing our realisations about Ai we are making the assumption that
the observables are just a particular realisation of the model (e.g.
Chap. 15.6 of Press et al. 1992). Then for each such realisation
we again find the most probable star by minimising χ2model in
Eq. (3). The final PDF is the frequency distribution of the intrinsic properties of the model stars that have been located in
this way. One may argue that the first step of finding the closest model star is not formally correct since it does not have a
corresponding Bayesian equivalent. However, we have found no
apparent differences in the results in tests where we exclude this
step in the procedure.
We use the PDF obtained from the Monte Carlo realisations to determine the distance. Due to the non-linearity of the
isochrones, as can be seen in Fig. 2, we expect the PDFs to be
Note that since J comes into the method twice (once for (J − Ks ) and
once in the distance modulus), we draw J and Ks separately to ensure
that the correlations are treated correctly.
asymmetric. In such cases the mode and the mean of the PDF are
not the same. Since the mean is a linear function3, we choose
to calculate the mean and standard deviations of M J (and distance d) from the Monte Carlo realisations. This gives us our
final determination for the distance to each star and its associated error. We also compared the method using the median of
the distribution of absolute magnitudes instead of the mean, and
found no significant differences.
We have not made use of any priors in this analysis. We
could have invoked a prior based on, for example, the luminosity function or mass function of stars in the solar neighbourhood. However, since the luminosity function of our sample is
not an unbiased selection from the true luminosity function in
the RAVE magnitude range (Zwitter et al. 2008), this makes the
task of quantifying our prior very difficult. We therefore choose
to adopt a flat prior in order to avoid any potential biases from
incorrect assumptions. However, it is hoped that by the end of
the RAVE survey it will have produced a magnitude limited catalogue, at which point it may become possible to invoke a prior
based on the luminosity function.
2.3. Testing the method
To test the method, we take a sample of 1075 model stars. This
set is large enough for testing purposes, allowing us to determine which kind of stars the method works best for. The sample
of 1075 model stars are taken from a coarsely generated grid
of isochrone models with metallicity [M/H] = 0. We convolve
[M/H] , T eff , log(g) and the colours with Gaussians with dispersions comparable to the error in the RAVE survey in order
to mimic our measurements (στ = 300 K, σlog(g) = 0.3 dex,
σ[M/H] = 0.25 dex, σ J ≈ σKs ≈ 0.02 mag; see Sect. 3.1).
The reason for choosing a fixed metallicity is twofold. In
Sect. 2.1 we have seen that different metallicities should give
similar results in terms of the precision with which the absolute
magnitude can be derived. Secondly, it also means that the results only have to be compared to one set of isochrones, making
it easier to interpret. Note that although one metallicity is used
to generate the sample, after error convolution, isochrones for all
metallicities are used for the fitting method.
We run the method described in the previous section on this
set of 1075 stars and analyse the results in the left column of
Fig. 3. The colours indicate the estimated errors on M J obtained
from our algorithm and are clipped to a value σ MJ = 1.25. The
middle row shows the results on a colour-magnitude diagram
(CMD). Stars on the main sequence and on the RGB appear to
have the smallest errors as expected (see Sect. 2.1). In the bottom
row, the difference between the input (i.e. model) and estimated
magnitude is plotted against the input magnitude of the model
star from which the estimate was derived, showing the deviation
from the input absolute magnitude grows with σ MJ , as expected.
The method appears to give reasonable results, showing no serious systematic biases. The left column of Fig. 3 shows that for
the main sequence and RGB stars in the RAVE data set we expect a relative distance error of the order of 25% (blue colours),
and for the other stars around 50−60% (green to red colours).
We run this procedure again, now testing the effect of reducing the error in T eff . If we decrease the error in T eff to 150 K,
we obtain the results shown in the middle column of Fig. 3. The
errors in M J do not seem to have changed much, except for a
very slight improvement for the main-sequence stars. If, on the
2
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3
The mean of a set of means is equal to the mean of the combined PDF.
M. A. Breddels et al.: Distance determination for RAVE stars
justifying our decision to carry out the model fitting using only
[α/Fe] = 0 models.
3. Application to RAVE data
3.1. Data
Fig. 3. Effect of the uncertainties in log(g) and T eff on the estimated absolute magnitude MJ . The main-sequence and RGB stars perform best.
Reducing the errors in log(g) has the largest effect. Left column: errors
similar to the RAVE dataset, σT eff 300 K and σlog(g) = 0.3. Middle column: reducing the errors in effective temperature, σT eff = 150 K. Right
column: reducing the errors in surface gravity, σlog(g) = 0.15. Top row:
the sample of 1075 stars, with colours indicating errors, clipped to a
value of σ MJ = 1.25. Middle row: CMD with colours indicating the
same errors as the top row. Bottom row: difference between input (i.e.
model) and estimated absolute magnitude versus input absolute magnitude. We include a running mean and dispersion. The colours correspond to the same scale as in the top row. The spread in this distribution
grows as the estimated uncertainty in MJ grows (as indicated by the
colour change).
other hand, we decrease the error in log(g) to 0.15 dex while
keeping the T eff error at 300 K, we obtain the results shown in
the right column in Fig. 3. This shows that the accuracy and
precision with which we can determine M J has increased significantly. Therefore, reducing the uncertainty in log(g) is much
more effective than a similar reduction in T eff and will result in
significant improvements in the estimate of the absolute magnitude. In future, high precision photometry from surveys such as
Skymapper’s Southern Sky Survey (Keller et al. 2007) may aid
the ability of RAVE to constrain the stellar parameters.
We carry out an additional test to quantify whether our decision to only fit to [α/Fe] = 0 models will bias our results.
To do this we generated three similar catalogues of model stars,
but with [α/Fe] = 0, 0.2, 0.4 dex. We then repeat the above procedure (as usual fitting to models with [α/Fe] fixed at 0) and
analyse the resulting distances. Reassuringly we find that there
is no difference between the accuracy of the three catalogues,
The Radial Velocity Experiment (RAVE) is an ongoing project
measuring radial velocities and stellar atmosphere parameters
(temperature, metallicity, surface gravity and rotational velocity) of up to one million stars in the Southern hemisphere.
Spectra are taken using the 6dF spectrograph on the 1.2 m
UK Schmidt Telescope of the Anglo-Australian Observatory,
with a resolution of R = 7500, in the 8500−8750 Å window.
The input catalogue has been constructed from the Tycho-2 and
SuperCOSMOS catalogues in the magnitude range 9 < I < 12.
To date RAVE has obtained spectra of over 250 000 stars, 50 000
of which have been presented in the most recent data release
(Zwitter et al. 2008).
This second RAVE data release provides metallicity
([M/H]), log(g) and T eff from the spectra, and has been crossmatched with 2MASS to provide J and Ks band magnitudes. The
(JK)ESO colours used for the Y 2 isochrones match the 2MASS
(JKs )2MASS colours very well, so no colour transformation is
required (Carpenter 2001).
We choose to use the J and Ks bands because they are in
the infrared (IR) and are therefore less affected by dust than
visual bands. To see whether extinction will be significant for
our sample we carry out a simple test using the dust maps of
Schlegel et al. (1998). If we model the dust as an exponential
sheet with scale-height 130 pc (Drimmel & Spergel 2001), we
find that given the RAVE field-of-view, a typical RAVE dwarf
located 250 pc away would suffer ∼0.03 mag of extinction in
the J-band. This corresponds to a distance error of ∼1%, which
is negligible compared to the overall uncertainty inherent in
our method. Reddening is similarly unimportant, with the same
typical RAVE star suffering ∼0.02 mag reddening in (J − Ks ).
Even if we only consider fields-of-view with |b| < 40◦ then
we find that the extinction for a star at a distance of 250 pc is
only 0.04 mag (with corresponding distance error of ∼2%). Note
that for future RAVE data releases it may be possible to use information from the spectra to include extinction corrections for
some individual stars (Munari et al. 2008).
The observed parameter values used for the model fitting
routine are the weighted average of the available values, where
the weight is the reciprocal of the measurement error:
j w jX j
Xweighted = ,
(4)
j wj
where X j are the measured values and w j = 1/σ2j the corresponding weight. The error in the average is calculated as:
σ2weighted = 1
·
2
j 1/σ j
(5)
For the RAVE data, T eff is determined only from the spectra,
i.e. not photometrically, which means that T eff and (J − Ks ) are
uncorrelated in the sense that they are independently observed.
Therefore we can use both T eff and (J − Ks ) in Eq. (3) to obtain
our distance estimate. The error in (J − Ks ) is small compared
to other colours, which means that adding further colours will
result in only a negligible improvement on the uncertainty of the
absolute magnitude. For this reason we only use this one colour.
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A&A 511, A90 (2010)
The current RAVE data release (Zwitter et al. 2008) does not
include individual errors for each star’s derived parameters and
so for the errors in [M/H], T eff and log(g) we take 0.25 dex,
300 K and 0.3 dex respectively. The errors in [M/H] and T eff are
reasonable averages for different types of stars of low temperature, as can be seen from Fig. 19 in Zwitter et al. (2008). Even
though our log(g) error estimate is slightly smaller compared to
this figure, our results do not show evidence of an underestimation in the distance errors (Sect. 3.3.1). In fact, repeated observations of certain stars in the RAVE catalogue indicate that these
errors may be conservative (Steinmetz et al. 2008). The RAVE
DR2 dataset has two metal abundances, one uncalibrated, determined from the spectra alone ([m/H]), and a calibrated value
([M/H]). The latter is calibrated using a subset of stars with accurate metallicity estimates and it is this value which we use in
the fitting method. As above we assume solar-scaled metallicities, which means that [α/Fe] = 0 and [M/H] = [Fe/H].
3.2. Determining distances to RAVE stars
We now use the data set described above to derive absolute magnitudes using our model fitting method (see Sect. 2.2).
The RAVE second data release (Zwitter et al. 2008) contains 51 829 observations, of which 22 407 have astrophysical
parameters. We first clean up the dataset by requiring that the
stars have all parameters required by the fitting method ([M/H],
log(g), T eff , J, Ks ), a signal to noise ratio S2N > 20, no 2MASS
photometric quality flags raised (i.e. we require “AAA”) and
the spectrum quality flag to be empty to be sure we have no
obvious binaries or cosmic ray problems. Although this latter
flag will eliminate clear spectroscopic binaries (132 individual
stars, 0.2%), our sample must suffer from binary contamination
given the estimated 37% binary fraction for F and G stars in the
Copenhagen-Geneva survey (Holmberg et al. 2009) or the much
lower estimates 6−14% of Famaey et al. (2005). In future the use
of repeated observations for the RAVE sample will give a better
understanding of the effect of binaries on, for instance, the T eff
and log(g) estimates (Matijevic et al. 2009).
Although most of the RAVE survey stars in this data release
are located at high latitude (with |b| > 25◦ ), there are a limited
number of calibration fields with |b| < 10◦ . We remove these
low-latitude fields from our analysis since they could suffer from
significant extinction which will bias our distance estimates.
For some stars multiple observations are available, these
are grouped by their ID, and a weighted average (Eq. (4)) and
corresponding error (Eq. (5)) for all radial velocities are calculated. The astrophysical parameters ([M/H], log(g) and T eff )
have nominal errors as described in Sect. 3.1. For these parameters an unweighted average is calculated but the error in the
average is kept equal to the nominal error. The total number of
independent sources matching these constraints is 16 645.
Once we have our clean sample of stars we first find the best
model star as described in Sect. 2.1. If it has a χ2model ≥ 6 (Eq. (3))
it is not considered further. This last step gets rid of the ∼3% of
stars that are not well fit by any model.
Our final sample has 16 146 sources which are used for the
model fitting method to obtain an estimate of the distance and
associated uncertainty for each star.
The distribution of uncertainties in the absolute magnitude
and the distance for this clean sample of 16 146 stars can be
found in Fig. 4 (black line). The x-axes are scaled such that the
uncertainties can be compared using σd /d ≈ σ MJ ln(10)/5 =
0.46σ MJ . The differences between the two histograms show that
the error in the apparent J magnitude does contribute to the
Page 6 of 16
Fig. 4. Error distribution (left) and cumulative plot (right) for MJ (top)
and distance (bottom). These distributions are for the clean sample of
16 146 stars (see Sect. 3.2). The black line includes all the stars, while
the grey line shows the distribution for main-sequence stars (defined
here as those with log(g) > 4).
relative distance error. In Fig. 5 we show how the uncertainties
behave for the different types of stars. The distribution of uncertainties for the sample is as follows: 25% (4037) of the stars have
relative (statistical) distance errors of <35%, while 50% (8073)
and 75% (12 110) have relative (statistical) errors smaller than
45% and 50% respectively. For main-sequence stars (which we
define here as those with log(g) > 4, the grey line in Fig. 4)
the distribution of uncertainties is: 25% (1744) have relative distance errors <31%, while 50% (3488) and 75% (5231) have relative errors smaller than 36% and 42% respectively.
The Y 2 isochrones do not model the later evolutionary stages
of stars, such as the horizontal branches and the asymptotic giant
branch. The red clump (RC), which is the horizontal branch for
Population I stars, is a well populated region in the CMD due
to the relatively long lifetime of this phase (∼0.1 Gyr) (Girardi
et al. 1998). Therefore we expect the RAVE sample to include
a non negligible fraction of RC stars. Using the selection criteria of Veltz et al. (2008) and Siebert et al. (2008), namely
0.5 < (J − Ks ) < 0.7 and 1.5 < log(g) < 2.5 we find about ∼10%
of the RAVE sample could be on the RC. This region is highlighted in Fig. 5 with a black rectangle. The distance to many
of these stars can be determined using the almost constant absolute magnitude of the RC (e.g. Veltz et al. 2008; Siebert et al.
2008). However, since there may be better ways to isolate the
RC region, we choose to determine the distances for all these
stars using our method. Therefore, in the rest of this paper we
make no distinction between RC and RGB stars. Nonetheless,
we recommend users to discard what they believe may be RC
stars, and possibly to determine their distances using the absolute magnitude of the RC.
M. A. Breddels et al.: Distance determination for RAVE stars
Fig. 5. Results after applying the model fitting method to the RAVE
data. Colours indicate the magnitude of the error in MJ . Only stars
with σ MJ < 1.0 are plotted. Isochrones for [M/H] = 0 are plotted for
comparison. Top: CMD of RAVE dataset showing that the stars on the
main sequence and RGB stars have the smallest errors. Bottom: log(T eff )
versus log(g), colour coding as in the top panel. The black rectangle
approximately highlights the area in which red clump (RC) stars are expected to be found. The assumed error in log(g) is 0.3 dex and in T eff
is 300 K. Note that although the RGB stars in this panel do not match
the [M/H] = 0 isochrones, they are more consistent with the isochrones
corresponding to their measured metallicities.
3.3. Testing of RAVE distances
In order to verify the accuracy of our distance estimates, we perform two additional checks using external data and observations
of the open cluster M 67.
3.3.1. Hipparcos
The best way to assess our distance estimates is through independent measurements. For calibration purposes a number of
RAVE targets were chosen to be stars previously observed by
the Hipparcos mission, which means that for these stars we will
have an independent distance determination from the trigonometric parallax. These stars are at the brighter end of the RAVE
magnitude range and are mostly dwarfs.
We take the reduction of the Hipparcos data as presented by
van Leeuwen (2007a,b) and cross-match these with our RAVE
stars. In order to maximise the number of RAVE stars we use
a preliminary dataset larger than the public release described
in Sect. 3.1; this dataset contains ∼250 000 stars, but has not
Fig. 6. Bottom: distance from our method versus Hipparcos distance,
the dashed line corresponds to equal distances. Top: histogram of relative distance differences between our distance and that of Hipparcos.
The dashed line shows the expected distribution given the quoted errors
from our method and Hipparcos. Note that the observed distribution is
narrower, indicating that our errors are probably overestimated for these
stars (see Sect. 3.3.1).
undergone the rigourous verification and cleaning of the public
data release. This cross-matching provides 624 stars for which
the Hipparcos parallax errors are less than 20% and our distance
errors are less than 50%. Note that when dealing with uncertain
trigonometric parallaxes it is well known that the corresponding
distance determinations are systematically underestimated (Lutz
& Kelker 1973). We correct for this using the prescription described in Sect. 3.6.2 of Binney & Merrifield (1998), in particular Eq. (3.51)4.
In the bottom panel of Fig. 6 we show a plot of our distance estimate (dRAVE ) vs. the Hipparcos distance (dHipparcos ).
4
A mistake is present in Eq. (3.51) of Binney & Merrifield (1998). The
correct expression
derived from the preceding
equation, which
can be gives /σ = /σ + (
/σ )2 + 4(5β − 4) /2, where and are the true and measured parallax respectively and β the slope of the
luminosity function power law (the prior).
Page 7 of 16
A&A 511, A90 (2010)
Fig. 7. Relative offset in distance from our method vs. the trigonometric parallax determination from Hipparcos, as function of log(g), [M/H] ,
(J − Ks ) and T eff . We include a running mean and dispersion.
Clearly there is some scatter in this distribution, but in the
top panel we quantify this by showing the distribution of
(dRAVE − dHipparcos )/dHipparcos . The curve shows the expected distribution given our error on dRAVE and approximating the error
on dHipparcos from the error on the parallax (the true error on
dHipparcos is non-trivial to calculate owing to the aforementioned
Lutz-Kelker bias). It can be seen that the predicted distribution
is broader than the observed one; if we assume our estimate of
the Hipparcos errors are reasonable, this discrepancy between
the two distributions indicates that our errors are probably overestimated. We believe this can be explained by the fact that only
the brightest RAVE stars have trigonometric parallaxes in the
Hipparcos catalogue. These brighter stars have higher S2N than
the average RAVE stars and so the true uncertainties on the stellar parameters are actually smaller than our adopted values. The
average S2N for these 624 stars is ∼64, which is twice the typical S2N ratio for RAVE stars; correspondingly the uncertainties on the stellar parameters will be smaller by a factor of 1.3
(Sect. 4.2.4 of Zwitter et al. 2008).
Page 8 of 16
We can quantify the overestimation in our distance errors for
these stars. The 3σ clipped standard deviation of the observed
distribution is 22.1% and that of the predicted distribution is
27.8%. To give the predicted distribution the same spread as the
observed distribution would require us to decrease the distance
errors from our method for these stars by ∼35%. Note that the 3σ
clipping of this distribution is necessary since a small fraction of
our distances are in significant disagreement with Hipparcos. Of
the 624 stars in this cross-matched sample, there are 3 with distance overestimates of more than 50%, however closer inspection shows they qualify to be RC stars (Sect. 3.2). One more star
qualifies as RC star and has a distance overestimate of 40%, and
one star with a log(g) = 2.8 has a distance overestimate of 20%.
The systematic overestimation for possible RC stars and RGB
stars is in agreement with our findings in the next section.
In Fig. 7 we show the distribution of (dRAVE −
dHipparcos )/dHipparcos as a function of the 2MASS colour (J − Ks )
and of the three main stellar parameters (T eff , [M/H], log(g)).
We see no clear systematic trends at a level of more than ∼15%
M. A. Breddels et al.: Distance determination for RAVE stars
in any of the properties shown here, which implies that our
method is producing reliable distances for main-sequence stars.
3.3.2. M 67 giants
The results from the previous section give us confidence the
method works well for nearby main-sequence stars, but give us
no indication of the validity of the distances to giant stars.
Our preliminary RAVE dataset includes a small number of
RGB stars which are members of the old open cluster M 67.
As the distance to M 67 is relatively well known, this makes a
perfect test case for these stars. M 67 has a distance modulus of
(m−M)V = 9.70, near-solar metallicities and an age of τ ≈ 4 Gyr
(VandenBerg et al. 2007).
We identify members of M 67 using the following criteria:
offset from the cluster centre of less than 0.55◦; heliocentric radial velocity within 3.3 km s−1 of the mean value of 32.3 km s−1
(Kharchenko et al. 2005), where this value of 3.3 km s−1 corresponds to three times the uncertainty in the mean velocity; signal to noise ratio S2N > 20; log(g) < 3.5. A total of 8 stars
pass these criteria. In Fig. 8 we show these members, where one
star is observed twice. For these stars our method gives a distance of ∼1.82 ± 0.27 kpc, more than twice the distance from
the literature (∼0.8 kpc; VandenBerg et al. 2007). Note however that the 4 stars at J ≈ 8.8 qualify as RC stars as defined
in Sect. 3.2. If we exclude these stars then the distance to M 67
is 1.48 ± 0.36 kpc. The distance estimate is now within 2 sigma
of the assumed real distance of 0.8 kpc, but still systematically
overestimated. This overestimation can be understood when one
considers the performance of the stellar models. In the bottom
panel we show the CMD of the members with a set of isochrones
for comparison. The black isochrone is for an age similar to that
of the M 67 population (4 Gyr) and of solar metallicity. At least
one or both of the predicted colour and absolute magnitude of
the stars is incorrect. In the top panel we show a plot of log(g)
vs. T eff , which shows that the stars do not lie on the isochrone
in this plane either. Although the stars are within 1 or 2σ from
the 4 Gyr isochrone, the deviation is systematic, particularly for
the brighter RGB stars. This discrepancy will clearly impair our
method and hence it is not surprising that our distances are affected. The difficulty of obtaining isochrones that match giants
is a long standing problem that is being addressed by various
authors (e.g. VandenBerg et al. 2008; Yadav et al. 2008).
Therefore, given the limitations of the models used in this
work, our distances for stars with log(g) < 3 should be treated
with caution. They can still be useful for analysing trends in the
data (Sect. 4), but distances to individual stars are likely to be
inaccurate. Note as well that our simplification to treat RC as
RGB stars will lead to an overestimation of their distance. We
return to the issue of stellar models in the discussion (Sect. 5.1).
3.4. 6D phase-space coordinates for stars in the RAVE
dataset
Besides providing distances to RAVE stars, we also provide full
6D phase-space information derived using the radial velocities
(from RAVE) and the archival proper motions contained in the
RAVE catalogue (from the Starnet2, Tycho2, and UCAC2 catalogues; see Zwitter et al. 2008).
We use the Monte Carlo techniques described above to calculate 6D phase-space coordinates assuming Gaussian errors
on the observed quantities (radial velocities, proper motions,
Fig. 8. Bottom: CMD of M 67 giants on top of theoretical solarmetallicity Y 2 isochrones, with the 4 Gyr isochrone in black. The
isochrones are spaced logarithmically in age between 0.01 to 15 Gyr.
Horizontal lines indicate 1σ uncertainties in (J − Ks ) and the uncertainties in the vertical direction are smaller than the size of the data-point.
Top: similar to top panel, except now for log(g) versus log(T eff ).
etc.). This is done using the transformations given by Johnson
& Soderblom (1987).
The coordinate system we use is a right-handed Cartesian coordinate system centred on the Galactic Centre (GC): the x axis
is aligned with the GC-Sun axis with the Sun located at x =
−8 kpc; the y axis pointing in the direction of rotation and the
z axis pointing towards the Northern Galactic Pole (NGP). The
velocities with respect to the Sun in the directions of (x, y, z) are
(U, V, W) respectively, with the rest frame taken at the Sun (such
that the Sun is at (U , V , W ) = (0, 0, 0)). Our final catalogue
also includes cylindrical polar coordinates (vρ, vφ , vz ), defined in
a Galactic rest frame such that the local standard of rest (LSR)
moves at vφ = −220 km s−1 . To transform from the rest frame
of the Sun to the Galactic rest frame, we use vLSR = 220 km s−1
for the LSR and take the velocity of the Sun with respect to the
LSR to be (10.0 km s−1 , 5.25 km s−1 , 7.17 km s−1 ) (Dehnen &
Binney 1998). A full description of the coordinate systems is
Page 9 of 16
A&A 511, A90 (2010)
4. Scientific results
Fig. 9. Distribution of uncertainties for velocity components U (solid
line), V (dashed line) and W (dotted line) velocities. This corresponds
to the clean sample of 16 146 stars (see Sect. 3.2). The black line includes all the stars, while the grey line shows the distribution for mainsequence stars (defined here as those with log(g) > 4).
given in Appendix B. An overview of the errors for U, V and W
are shown in Fig. 9. We find that 7139 (44% of the 16 146 ) stars
have errors less than 20 km s−1 in all three velocity components,
and 11 742 (73%) have errors less than 50 km s−1 . For the mainsequence stars this is 5425 (78% of the 6975 ) and 6832 (98% of
the 6975 ) respectively.
3.5. The catalogue
Our catalogue is available for download from the webpage
http://www.astro.rug.nl/~rave/ and is also hosted by the
CDS service VizieR5 . We aim to update the catalogue as future
RAVE data releases are issued. The format of the catalogue is
described in full in Appendix A.
5
http://webviz.u-strasbg.fr
Page 10 of 16
The main components of our Galaxy are the bulge, the halo
and the thin and thick disks. The thin disk has a scale height
of ∼300 pc, while the thick disk scale height is ∼1 kpc (e.g.
Jurić et al. 2008). The disk is known to be dominated by metal
rich stars, while halo stars are in general metal poor (see Wyse
(2006) for a recent review). To see if this is reflected in the RAVE
data, we will now focus on how the metallicity and kinematics
change as a function of distance from the plane.
In Fig. 10 we show the spatial distribution of stars in the
RAVE dataset, where we have restricted ourselves to stars with
errors of less than 40% in distance. As expected, we see a strong
concentration of stars within 1 kpc, illustrating that most of our
stars are nearby disk dwarfs. However, there are also a number of
stars at much larger distances, which are giants probing into the
Galactic halo (although one should bear in mind that our giant
distances are likely to be unreliable; see Sect. 3.3.2).
Given this large span of distances, we can investigate the
change in metallicity as we move out of the Galactic plane. Since
we still have stars with non-negligible errors in distance, this
analysis will be subject to contamination from stars at different
distances, so we show only the relevant trends in our data. The
resulting distribution of metallicity for three |z| bins is shown in
Fig. 11 for stars with relative distance error less than 75%. It
is clear that most of the stars in the |z| < 1 kpc bin are consistent with a solar-metallicity thin-disk population, but as we move
away from the plane the mean metallicity decreases. In particular, a tail of metal-poor stars is evident for |z| > 3 kpc, consistent
with a halo population. The trends that we are seeing are similar
to those seen by Ivezić et al. (2008), where the metal-poor halo
becomes apparent at [M/H] <
∼ −1 for |z| >
∼ 2 kpc.
We now analyse the velocities of stars in our sample, restricting ourselves to a high-quality subset of 5020 stars. For this sample we only use those stars with distance error less than 40%,
proper motion error less than 5 mas yr−1 (in both components)
and radial velocity error less than 5 km s−1 .
In Fig. 12 we have plotted the average vφ (where −220 km s−1
corresponds to the LSR) in different bins of |z|. It shows a decreasing rotational velocity as we move away from the Galactic
plane, which can be explained by a transition from a fast rotating
disk component, to a non-rotating (or slowly-rotating) halo. As
before, owing to our uncertainties in the giant distances, this plot
should only be used to draw qualitative conclusions.
For nearby dwarfs (log(g) > 4) the errors in velocity
are relatively small, therefore we refine our sample further
by considering a volume-limited sample. We use a cylindrical volume centred on the Sun with a radius of 500 pc and
a height of 600 pc (300 above and below the Galactic plane).
This sample, which contains 3249 stars, has average errors of
(8.2 km s−1 , 6.3 km s−1 , 5.1 km s−1 ) in the (U, V, W) directions,
respectively. The velocity distributions for these stars are shown
in Fig. 13 and the corresponding means and velocity dispersions
are given in Table 1. The uncertainties are obtained by a bootstrap method. Note that these distributions will be broadened by
the observational errors, but we have not taken this into account
when calculating these variances. For this sample, we also tabulate the full velocity dispersion tensor σi j . As has been found by
previous studies (e.g. Dehnen & Binney 1998), the σUV term is
clearly non-zero (σ2UV = 108.0 ± 25.7 km2 s−2 ). For this component we can calculate the vertex deviation,
⎞
⎛
σ2UV ⎟⎟⎟
⎜⎜⎜
1
⎟⎠ ,
⎜
lv = arctan ⎝2 2
(6)
2
σU − σ2V
M. A. Breddels et al.: Distance determination for RAVE stars
Fig. 10. The RAVE stars in galactic coordinates, the circle with label GC indicates the galactic centre (which we have assumed to be at a distance
of 8 kpc from the Sun). We have only plotted those stars with distance error less than 40%.
Fig. 11. Normalised metallicity distribution for stars in different bins of
height above the Galactic plane, where we are only showing stars with
distance error less than 75%. As expected, stars further away from the
Galactic plane are more metal poor.
which is a measure of the orientation of the UV velocity ellipsoid. We find lv = 8.7 ± 2.0◦ , which is comparable to the value
of 10◦ found for stars with (B − V) >
∼ 0.4 in the immediate solar
neighbourhood by Dehnen & Binney (1998). The uncertainties
on the other two cross-terms (σ2UW and σ2VW ) are too large to
allow us to detect any weak correlations that might be present.
Close inspection of the middle panel of Fig. 13 shows an
asymmetric distribution for the V component, with a longer tail
towards lower velocities. This is due to two effects. The first is
that we are seeing the well-known asymmetric drift, where populations of stars with larger velocity dispersions lag behind the
LSR (Binney & Merrifield 1998). Secondly, it is known that the
velocity distribution of the solar neighbourhood is not smooth
(see, e.g. Chereul et al. 1998; Dehnen 1998; Nordström et al.
2004). This issue is further illustrated in Fig. 14, where we show
the distribution of velocities in the UV-plane. A slight overdensity of stars around U ≈ −50 km s−1 , V ≈ −50 km s−1 can
be seen which will affect the symmetry of the V velocity component. This over-density is called the Hercules stream, and is
Fig. 12. Rotational velocity as a function of |z| for the high-quality
subset of 5020 stars (see Sect. 4). The error bars indicate 1σ uncertainty in the means. Note that the LSR has been assumed to move with
vφ = −220 km s−1 .
thought to be due to a resonance with the bar of our Galaxy
(Dehnen 2000; Fux 2001).
It should be noted that all velocities are with respect to the
Sun, which implies that the Sun’s U and W velocity with respect
to the LSR are the negative of the mean U and W in our sample. Due to the asymmetric drift, the V velocity of the complete
sample of stars is not equal to the negative of the V velocity of
Sun with respect to the LSR (Binney & Merrifield 1998). The
velocities and dispersions are in reasonable agreement with the
results of Famaey et al. (2005) and Dehnen & Binney (1998)
even though we are using different samples from those examined in these previous studies (e.g. probing different volumes or
types of stars).
5. Discussion
5.1. The influence of the choice of stellar models
The method described in Sect. 2.2 clearly relies on the ability
of stellar models to accurately predict the observed parameters.
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A&A 511, A90 (2010)
Fig. 13. Velocity distributions for the U, V and W components (histogram) and the best fit Gaussian (solid line) for high-quality volume-limited
sample of 3249 stars (see Sect. 4). The velocity distributions for U and W are symmetric, showing a slight negative mean U and W owing to the
solar motion with respect to the LSR. As expected, the V component shows an slight asymmetry, having a longer tail towards the slower rotating
stars.
Table 1. Means, standard deviations and covariances for U, V and
W velocities corresponding to the high-quality volume limited sample
of 3249 stars (see Sect. 4).
Mean
U
V
W
(km s−1 )
Standard Deviation
−12.0 ± 0.6
σU
−20.4 ± 0.5
σV
−7.8 ± 0.3
σW
(km s−1 )
36.7 ± 0.6
25.6 ± 0.8
19.1 ± 0.4
Covariance
(km2 s−2 )
σ2UV
108.0 ± 25.7
σ2UW
−19.7 ± 17.3
σ2VW
12.8 ± 16.2
Therefore it is worth briefly discussing the potential difficulties
which may arise from this assumption.
As was discussed in Sect. 2.2 we have chosen to use the
Yale-Yonsei (Y 2 ) models (Demarque et al. 2004), but there are
several groups who make stellar models. In Fig. 15 we compare
isochrones (with age 5 Gyr, Z = 0.019, [α/Fe] = 0) from the
following three groups: the Y 2 group (Demarque et al. 2004),
the Padova group (Marigo et al. 2008) and the Dartmouth group
(Dotter et al. 2008). The latter paper can be consulted for a more
detailed comparison of the various groups’ theoretical models
(see also Glatt et al. 2008).
In general the three curves in the log(T eff ) − log(g) plane and
log(T eff ) − M J plane show reasonably good agreement, certainly
within the observational errors of the RAVE data (see Sect. 3.1).
The largest discrepancy is for the cool dwarfs (log(T eff ) < 3.65),
but we do not believe this should have any significant effect on
our results as we have very few stars in this regime. When one
considers the (J − Ks )−M J plane the situation is less satisfactory,
probably due to the T eff -colour transformations.
To assess whether our decision to use the Y 2 models has any
serious effect on our results, we repeat the analysis presented in
Sect. 3.3 using the Dartmouth models. We find that this has very
little influence; there is no noticeable improvement for either the
Hipparcos dwarfs or the M 67 giants. Therefore we conclude that
our method is not particularly sensitive to the choice of stellar
models. However, one should still bear in mind that, by definition, our method will be limited by any problems or deficiencies
in the adopted set of isochrones.
Page 12 of 16
5.2. Comparisons to other work
Klement et al. (2008, hereafter K08) have used a different
method to derive distances for RAVE stars, seemingly obtaining significantly smaller errors than ours. They calibrated a
photometric distance relation (relating VT − H to MV ) using
stars from Hipparcos catalogue with accurate trigonometric parallaxes, combined with photometry from Tycho-2, USNO-B
and 2MASS. This method was then applied to the first RAVE
data release (DR1; Steinmetz et al. 2006). Although the number of stars analysed by K08 is similar to that considered here
(∼25 000), they obtain ∼7000 stars with distance errors smaller
than 25%, while we have only 431 stars with distance errors
smaller than 25%.
The K08 method relies on stars being on the main sequence.
However, from the values of log(g)we can now show that of order half the RAVE stars are giants: in Fig. 16 we show the cumulative distribution of log(g), showing that main-sequence stars
(log(g) > 4, see also Fig. 1) are only ∼40% of the whole sample. Therefore it is clear that a large fraction of the RAVE sample are giants, subgiants or close to the main-sequence turn-off.
This will undoubtedly affect the results presented in K08. For
example, their plot of the UW velocity distribution is evidently
suffering from significant systematics as can be seen from the
correlation between the U and W velocities. Previous studies of
local samples of stars have not found such a correlation. Our
distribution of UW shows no such strong correlation (Fig. 14)
and σUW is consistent with 0. Even in samples of stars out of
the plane where one might expect correlations to appear, there is
no evidence for such a pronounced level of correlation (Siebert
et al. 2008).
As well as the problem of misclassified giant stars, additional
factors that will adversely affect the K08 distances include: the
metallicity distribution of the local RAVE sample will probably
differ from that of Hipparcos due to the fact that RAVE probes a
different magnitude range (and hence volume); or that K08 use
the V-band which is more prone to reddening than our choice of
(J − Ks ). With regard to this latter point, we can repeat the simple analysis presented in Sect. 2.2. For a typical star 250 pc away,
given the RAVE field-of-view the dust maps of Schlegel et al.
(1998) predict extinction of ∼0.1 mag in V (with corresponding
distance error of ∼5%) and reddening of ∼0.1 mag in (V − H).
M. A. Breddels et al.: Distance determination for RAVE stars
Fig. 14. The UV, UW and VW velocity distributions for the high-quality volume-limited sample of 3249 stars (see Sect. 4). The upper-left panel
shows isodensity contours for the UV plane, where the contours contain 2, 6, 12, 21, 33, 50, 68, 80, 90, 99 and 99.9 percent of the stars. The
red + symbol marks the LSR (Dehnen & Binney 1998) and the green symbol marks the solar velocity (0, 0).
6. Conclusion
We have presented a method to derive absolute magnitudes, and
therefore distances, for RAVE stars using stellar models. It is
based on the use of stellar model fitting in metallicity, log(g),
T eff and colour space.
We find that our method reliably estimates distances for
main-sequence stars, but there is an indication of potential systematic problems with giant stars owing to issues with the underlying stellar models. The uncertainties in the estimated absolute
magnitudes for RGB stars are found to depend mainly on the
uncertainties in log(g), while for main-sequence stars the accuracy of T eff is also important (Sect. 2.3). For the RAVE data the
uncertainties in log(g) and T eff give rise to relative distance
uncertainties in the range 30%−50%, although from crossmatching with Hipparcos (Sect. 3.3.1) it appears that our uncertainties may be overestimated for the brighter stars (with higher
signal-to-noise spectra). It is important to note that that some
10% of the RAVE stars may be on the red clump, but these are
treated as RGB by our pipeline, and hence their distances may
be systematically biased.
As can be seen in the results section (Sect. 4), the data accurately reflect the known properties of halo and disk stars of the
Milky Way. A variation in metallicity and vφ was found away
from the Galactic plane, corresponding to an increase in the
fraction of metal-poor halo stars. Existing substructure in the
Page 13 of 16
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Fig. 15. A comparison of isochrones from three separate groups: Yale-Yonsei (black), Padova (red), Dartmouth (green). We have chosen isochrones
with age 5 Gyr, Z = 0.019, [α/Fe] = 0.
for their helpful suggestions. M.A.B. and A.H. gratefully acknowledge the
the Netherlands Research School for Astronomy (NOVA) for financial support. M.C.S. and A.H. acknowledge financial support from the Netherlands
Organisation for Scientific Research (NWO). M.C.S. acknowledges support
from the STFC-funded “Galaxy Formation and Evolution” program at the
Institute of Astronomy, University of Cambridge.
Funding for RAVE has been provided by the Anglo-Australian Observatory, by
the Astrophysical Institute Potsdam, by the Australian Research Council, by
the German Research foundation, by the National Institute for Astrophysics
at Padova, by The Johns Hopkins University, by the Netherlands Research
School for Astronomy, by the Natural Sciences and Engineering Research
Council of Canada, by the Slovenian Research Agency, by the Swiss National
Science Foundation, by the National Science Foundation of the USA (AST0508996), by the Netherlands Organisation for Scientific Research, by the
Science and Technology Facilities Council of the UK, by Opticon, by Strasbourg
Observatory, and by the Universities of Basel, Cambridge, Groningen and
Heidelberg.
The RAVE web site is at www.rave-survey.org.
Fig. 16. Cumulative distribution of log(g), the black line shows the %
of stars below a certain log(g), while the dashed grey line shows stars
above a certain log(g).
UV velocity plane was recovered, as was the vertex deviation.
Upon completion the RAVE survey will have observed a factor
of up to ∼20 times more stars than analysed here. Clearly this
will be a hugely valuable resource for studies of the Galaxy.
In future the Gaia satellite mission (Perryman et al. 2001)
will revolutionise this field, recording distances to millions of
stars with unprecedented accuracy. However, for large numbers
of Gaia stars it will not be possible to accurately constrain the
distance due to them being too far away or too faint, which implies that it is crucial to develop techniques such as ours for reliably estimating distances.
In the near term it will be possible to improve the accuracy
of our pipeline by calibrating it through observations of clusters;
a technique which has been used with great success by the Sloan
Digital Sky Survey (Ivezić et al. 2008). Within the RAVE collaboration a project is underway to obtain data for cluster stars
(e.g. Kiss et al. 2007) and we aim to incorporate this into future
analyses. This may allow us to reduce or remove the reliance on
stellar models, which will lessen one of the major sources of uncertainty in our work. Our pipeline will allow us to fully utilise
current surveys such as RAVE, and also places us in an ideal position exploit future large-scale spectroscopic surveys that will
be enabled by upcoming instruments such as LAMOST.
Acknowledgements. We thank the referee for useful suggestions that helped improve the paper. We also thank Heather L. Morrison and Michelle L. Wilson
Page 14 of 16
Appendix A: Description of RAVE catalogue
with phase-space coordinates
We present the results of our distance determinations and corresponding phase-space coordinates as a comma separated values (CSV) file, with headers. The columns are described in
Table A.1. See Steinmetz et al. (2006); Zwitter et al. (2008) for
a more detailed description of the RAVE data.
Appendix B: Coordinate systems
The x
, y
, z
coordinate system we use is a right handed
Cartesian coordinate system centred on the Sun indicating positions, with the x
axis pointing from the Sun to the Galactic
Centre (GC), the y
axis pointing in the direction of rotation
and the z
axis pointing towards the Northern Galactic Pole
(NGP). The x, y, z coordinate system is similar to the x
, y
, z
coordinate system, but centred on the GC, assuming the Sun
is at (x, y, z) = (−8 kpc, 0, 0). An overview can be found in
Fig. B.1 with Galactic longitude (l) and latitude (b) shown for
completeness.
The velocities with respect to the Sun in the directions of
x, y, z are U, V, W respectively. For velocities of nearby stars,
a Cartesian coordinate system will be sufficient, but for large
distances, a cylindrical coordinate system makes more sense for
disk stars. To calculate these coordinates, we first have to transform the U, V, W velocities to the Galactic rest frame, indicated
by v x , vy , vz as shown in Fig. B.2. Assuming a local standard of
rest (LSR) of vLSR = 220 km s−1 , and the velocity of the Sun
M. A. Breddels et al.: Distance determination for RAVE stars
Table A.1. A full description of the catalogue.
Field name
OBJECT_ID
RA
DE
Glon
Glat
RV
eRV
pmRA
pmDE
epmRA
epmDE
T eff
nT eff
log g
n log g
MH
nMH
MHcalib
nMHcalib
AM
nAM
Jmag
eJmag
Kmag
eKmag
Mj
eM j
distance
edistance
xGal
exGal
yGal
eyGal
zGal
ezGal
U
eU
V
eV
W
eW
vx Gal
evx Gal
vy Gal
evy Gal
vz Gal
evz Gal
Vr
eVr
Vφ
eVφ
Units
dex
Type
string
float
float
float
float
float
float
float
float
float
float
float
int
float
int
float
dex
int
float
deg
deg
deg
deg
km s−1
km s−1
mas yr−1
mas yr−1
mas yr−1
mas yr−1
Kelvin
log( cm
)
s2
dex
mag
mag
mag
mag
mag
mag
kpc
kpc
kpc
kpc
kpc
kpc
kpc
kpc
km s−1
km s−1
km s−1
km s−1
km s−1
km s−1
km s−1
km s−1
km s−1
km s−1
km s−1
km s−1
km s−1
km s−1
km s−1
km s−1
int
float
int
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
float
Description
RAVE internal identifier
Right ascension (J2000)
Declination (J2000)
Galactic longitude
Galactic latitude
Weighted mean of available radial velocities
Weighted error of available radial velocities
Proper motion RA
Proper motion DE
Error proper motion RA
Error proper motion DE
Arithmetic mean of available temperatures
Number of observations having T eff
Arithmetic mean of available surface gravities
Number of observations having log(g)
Arithmetic mean of RAVE uncalibrated metallicity ([m/H])
abundance
Number of observations having [m/H]
Arithmetic mean of RAVE calibrated metallicity ([M/H] )
abundance
Number of observations having [M/H]
Arithmetic mean of RAVE alpha enhancement ([α/Fe])
Number of observations having [α/Fe]
2MASS J magnitude
error on Jmag
2MASS Ks magnitude
error on Kmag
Absolute magnitude in J band (from fitting method)
Error on MJ
Distance from MJ and J
Error on distance
Galactic x coordinate2
Error on x
Galactic y coordinate2
Error on y
Galactic z coordinate2
Error on z
Galactic velocity on x
direction w.r.t the Sun (U)2
Error on U
Galactic velocity on y
direction w.r.t the Sun (V)2
Error on V
Galactic velocity on z
direction w.r.t the Sun (W)2
Error on W
Galactic velocity on x direction in Galactic rest frame (vx )2
Error on vx
Galactic velocity on y direction in Galactic rest frame (vy )2
Error on vy
Galactic velocity on z direction in Galactic rest frame (vz )2
Error on vz
Galactic velocity on ρ direction in Galactic rest frame (vρ )2
Error on vρ
Galactic velocity on φ direction in Galactic rest frame (vφ )2
Error on vφ
Notes. (2) See Sect. 3.4 for a description.
Page 15 of 16
A&A 511, A90 (2010)
z
φ
z
y
l
b
y
x
ρ
GC:(0, 0, 0)
x
Sun:(−8, 0, 0)
Fig. B.1. Overview of the Galactic coordinates. The Sun is found at
(x, y, z) = (−8, 0, 0). l and b are the Galactic sky coordinates.
vz
vφ
W
V
U
vy
vx
vρ
GC:(0, 0, 0)
Sun:(−8, 0, 0)
Fig. B.2. Overview of Galactic coordinate systems. U, V, W velocities
are with respect to the Sun and are aligned with the x
, y
, z
coordinate system. vx , vy , vz are Cartesian velocities, and vρ , vφ are cylindrical
velocities, both with respect to the Galactic rest frame.
with respect to the LSR from Dehnen & Binney (1998), we find:
v x = U + 10.0 km s−1 ,
vy = V + vLSR + 5.25 km s−1 ,
(B.1)
(B.2)
vz = W + 7.17 km s−1 .
(B.3)
The relations between Cartesian (x, y, z) and cylindrical coordinates (ρ, φ, z) are:
ρ cos(φ),
(B.4)
ρ sin(φ),
(B.5)
z,
(B.6)
x2 + y 2 ,
(B.7)
y
tan(φ) = ·
(B.8)
x
We can use this to find the velocities in the directions of ρ and φ:
x
y
z
ρ2
=
=
=
=
dρ xv x + yvy
=
,
dt
ρ
dφ xvy − yv x
vφ = ρ
=
·
dt
ρ
vρ =
(B.9)
(B.10)
Note that the direction of φ is anti-clockwise, meaning that the
LSR is at (vρ , vφ , vz ) = (0 km s−1 , −220 km s−1 , 0 km s−1 ).
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